I am searching for C# library which has code that builds spatial index in memory based on geometry bounds and enables fast searching for all geometry inside given bounds.
I prefer free library.
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There is a C#/.NET port of JTS Topology Suite: https://github.com/NetTopologySuite/NetTopologySuite
Here's the index classes: https://github.com/NetTopologySuite/NetTopologySuite/tree/develop/NetTopologySuite/Index
Maybe try googling for specific indexing methods. For example, when I Google for
C# r-tree this is the first result.
Another option is to use SQLite + Spatialite in memory. Create a table with a geometry column and a spatial index and insert your geometries there. Then use SQL queries to get the matching geometries.